1

Grade 5MATHEMATICS

EssentialsWeekby

Week WEEK

Using Numbers inPowerful Ways

Package A contains 5 pounds of hamburgermeat for $4.95.

Package B contains 3 pounds of hamburgermeat for $3.87.

Which is the better buy?

InvestigationsLet's find out about our class. What is the typicalfifth grade student like? What do we mean by"typical?" What questions do we want to answerabout ourselves?

Here's a possible plan of action:

1. Complete the census form on the back of thispage.

2. Decide what question(s) you will use to helpdescribe a typical fifth grade student. Determinehow you will collect your data.

3. Write a paragraph describing a typical fifth graderat your school.

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2

3

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Math TriviaThe ancient Greeks believed that if you studiednumbers you had to be a peson who did notneed to work because you would probably be aperson who was interested in strange andwonderful things. Who studies numbers today?

Fraction Fun

1

For Further StudyWhat is a census and how is it used?

1- = ++ 234

(4th review)

If the red pattern block shape represents three-fifthsof a shape, what does the whole look like?

If two-fifths of the shape costs $0.50, how muchwould the whole shape cost?

If one-fifth of the shape weighs 12 ounces, howmuch will the whole weigh?

(1.03)

(1.03)

2

FIFTH GRADE CENSUS

Name ___________________________________________________________________________First Middle Last Name

Date of Birth: __________________________________ Height: _________________________Month Date Year

Birth Weight: _______________________ Length at Birth: ________________________

Place of Birth ____________________________________________________________________City County State

Current Address __________________________________________________________________Street

________________________________________________________________________________City State Zip Code

Home Telephone Number: _________________________e-mail____________________________

Number of people who live at this address: _________________

Number of brothers: __________ Number of sisters: __________

Hair color: _____________ Eye color: ____________ Shoe Size: ___________

Right handed or left handed? __________

Circle grades attended at this school: K 1 2 3 4 5

How do you usually come to school? (check one) __ Walk __ Ride Bike __ Bus __ Car __ Other

Do you have a pet(s)? ___ No ___ Yes If yes, please describe:

________________________________________________________________________________

________________________________________________________________________________

What is your favorite: Subject in School: ______________________________________________

At Home Activity: ______________________________________________

Sport: ________________________________________________________

Television Program: ____________________________________________

Musical Group: ________________________________________________

3

Solve this!1- = ++ 234

Keeping Skills Sharp

1. 23 + 146

2. 287 - 194

3. 5 x 23

4. 804 ÷ 4

5. When Joe was 5 years old, his father was 34. How old was thefather when Joe was born?

6. Sal bought 2 boxes of cookies for $1.69 each. What was the totalbill?

7. Write the largest possible 3-digit number using 4, 5, 6.

8. What is the sum of two hundred sixty and one hundred eight?

There are 18 students from Mr. Bishop’s class seated in a circle.They are evenly spaced and numbered in order.

Who is directly opposite student #1?Who is directly opposite student #5?Who is directly opposite student #18?

If, in Mr. Simmons’ class, pupil 47 is opposite pupil 16 whenthe group is seated in a circle, how many students are in this PEclass?

(1.03)

4

Grade 5

To the Teacher WEEK

Keeping Skills SharpMental Math Directions to Students: Number your paper from1 to 10. Write your answers as the questions are calledout. Each question will be repeated only once.

1

Commentary on Investigations:The census should be kept to access throughout the year. Do not try to graph all of these categories this week.The information from the census can also be used to form a class database.

Before having your students look at any of these data, be sure the students understand the difference betweencategorical and numerical data. Data that are words or categories are called categorical data, for example, wherea person is born or a student’s hair color. Data that are numbers are called numerical data, for example, aperson’s height or number of brothers and sisters.

Misconception ALERT!Watch out for students using the count to find the range, median, or mean of categorical data. With categoricaldata the only accurate measure of central tendency is MODE.EXAMPLE: 8

76543210

Red Green Blue Yellow (favorite color)

The mode is blue. There is no range, median or mean. Students may try to say the range is 7 or 8 (using they-axis, which is a label of count, not the actual data.) They may also try to say the range is red to yellow;however, the range is always a number. There is no mean with categorical data because the words cannot beadded and divided. There is also not a median since the definition for median is the middle number in a set ofordered data.

Solve This: #10 is across from #1, #14 across from #5 and #9 is across from #18.62 students in PE class. Suggested Strategy: Draw a picture.

1. 169 5. 29

2. 93 6. $3.38

3. 115 7. 654

4. 201 8. 368

1. (5 - 3) x 7 + 62. 4 + 2 x 5 - 33. Word form 2374. Round to nearest ten: 835. Number of days in this month6. number of sides on a hexagon7. Width of pencil: centimeter or meter8. Length of notebook paper: foot or yard9. 1/2 dozen10. Number of years in a century

123456712345671234567123456712345671234567123456712345671234567

123456712345671234567123456712345671234567123456712345671234567123456712345671234567

123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567

123456123456123456123456123456

(cou

nt)

5

Grade 5MATHEMATICS

EssentialsWeekby

Week WEEK

Using Numbers inPowerful Ways

InvestigationsPalindromes are words or numbers that read the samebackwards and forwards.

Examples of Palindromes:

Words Numbers

race car 1991

Rise to vote sir 34543

Try this:

1. Take any 2-digit (or greater) numberand add the digits in reverse order to that number.

2. Continue this process with eachsuccessive sum until you get a numerical palindrome.

Examples: 9023

245 + 3209

+542 12232

787 + 23221

35453

3. Now choose 3 other numbers. Addthe numbers and their reversals untilyou get palindromes.

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2

3

4

Math Trivia

Fraction Fun

2

For Further StudyTry to discover a number sentence that is the samewhen you read its digits from either direction, suchas 10989 x 9 = 98901

1- = ++ 234

A boxing ring is a square with amaximum perimeter of 80 feet. What isthe area of a boxing ring with themaximum perimeter?

(1.03)

(1.03)

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1234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901

(1.03)

What fraction of this figure isshaded? How do you know?

Regular number cubes are sometimescalled seven cubes. Can you tell why?

(1.03)

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Putting Your Calculator To WorkDirections: During the week try to solve all of these problems. If you have trouble getting started, talk toa friend. Choose one of the problems, and write a letter explaining how you figured out the solution.

(1.03)

A stoplight flashes red for50 seconds, yellow for 5 seconds,and green for 65 seconds.

In a 24-hour period, how long is the light red?

Sean passed a bowl of peanuts around to 11 friends. Counting Sean,there were twelve people.) Sean took 1 peanut, his 1st friend took 3peanuts, the 2nd friend took 5 peanuts, and so on, until the 12th persontook peanuts and the bowl was empty.

How many peanuts were in the bowl in the beginning?

• How many days are there inone million seconds?

• If human life expectancy is 75years, how many hours is that?

• About how longwould the line beif the fifth gradersin your class laiddown head to toeto create a longline of students?

7

Solve this!1- = ++ 234

Keeping Skills Sharp

How many ways can the librarian arrange these books on a shelf?

1. 16 + 243 + 9

2. 60 x 7

3. 470 - 246

4. Round to the nearest 10: 461

5. What is the value of 5 in 12,584?

6. (5 x 6) + 3 = ?

7. Write in order from least to greatest : 438 348 843 483

8. Jana paid 50 cents for a pack of 14 baseball cards and 75 cents fora pack of 25 baseball cards. How many baseball cards did shebuy?

A

BC

D

(1.03)

8

Grade 5

To the Teacher WEEK

Keeping Skills SharpMental Math Directions to Students: Number your paper from1 to 10. Write your answers as the questions are calledout. Each question will be repeated only once.

2Solve this: Special for this week is a permutation because the listing of the order isimportant. The students may list all of the ways or create a tree diagram.

Help the students see the importance of using good order when making a list.

Example: ABCD, ABDC, ACBD, ACDB, ADBC, ADCB. Continue with the other 3letters for 24 ways! This may also be a good time to introduce factorial notation but onlyif you feel your students are ready to discuss this. Since this is a permutation with 4choices, it is a 4 factorial. The shorthand notation for factorial is an exclamation point.So 4! is called 4 factorial.

4! = 4 x 3 x 2 x 1= 24

There are 24 ways to arrange these 4 books on the shelf.

Suggested strategy: Make a list.

1. 268 5. 500

2. 420 6. 33

3. 224 7. 348, 438, 483, 843

4. 460 8. 39

1. (18 - 9) x 7 + 42. (13 - 5) x (6 - 5)3. Word form for: 1084. Round to nearest ten cents: 37¢5. Factors of 66. Geometric figure: shape of a soup can7. Number of centimeters in a meter8. Number of quarts in a gallon9. Number of quarters in $2.0010. Number of tens in 320

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Grade 5MATHEMATICS

EssentialsWeekby

Week WEEK

Using Numbers inPowerful Ways

Shuffle the numbered cards of an ordinary deckof cards (aces equal 1). Pick out one card to bethe answer card. Then deal off the top fourcards to use for an equation. Try to use 2, 3, orall 4 cards to form an equation. Example:Answer card is 4. Equation cards are 2, 6, 8,and 10. Possible equations are

(10 + 6 - 8 ) ÷ 2 = 4 or 8 +2 - 6 = 4 or

8 ÷ 2 = 4. Assign 5 points if you use all 4 cardsto make an equation, 3 points for using 3cards, and 1 point for using only 2 cards.

InvestigationsWorking with a partner, can you find one or more ofthese:

1. Odd 3-digit numbers with the sum of the

digits = 5.

2. Number of times the digit 5 is written whenyou write from 1to 1000.

3. Even 3-digit numbers greater than 700 whosedigits total 11.

4. Multiples of 5 that are 3-digit numbers whosedigit product is 90.

In each case, write an explanation of how you figuredthese out.

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Math Trivia

Fraction Fun

3

For Further StudyCan you create a subtraction problem using all thenumber tiles 0-9?

1- = ++ 234

(1.03)

(1.03)

How many triangles are in this shape?

(3.01)

This shape represents five-eights of awhole. What does one-half look like?

If the area of the given shape is 30square cm, what is the area of thewhole?

(1.03)

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(1.0

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11

Solve this!1- = ++ 234

Keeping Skills Sharp

1. $4.03 - $2.17

2. 36 + 298 + 7 + 314

3. 245 ÷ 3

4. A wagon train could travel 19 miles a day.How far could it travel in 6 days?

5. The Pony Express rider rode 5 horses each for 17 miles.Did he ride more or less than 100 miles?

6. Write the largest possible even number using digits, 1, 2, and 3.

7. 2300 - 1065

8. (3 x 8) + 7 =

9 9 9 (1.03)

Use the digits 1 to 9, onceeach in the square, andmake a sum of 999.

12

Grade 5

To the Teacher WEEK

Keeping Skills SharpMental Math Directions to Students: Number your paper from1 to 10. Write your answers as the questions are calledout. Each question will be repeated only once.

3

SOLVE THIS:One possible solution is:

584 136

+ 279 999

The students should discover more possibilities.Hint: Instead of making a sum of 9, the students need to make 19 for the last 2 digitsof the number. Example: 4 + 6 + ? = 19 (carry the one to the tens column).

Suggested Strategy: Guess and check

Math Trivia: twelve triangles

1. 5 x 2 x 62. 4 x 2 x 73. Word form for: 4094. Round to nearest ten: 3745. Factors of 116. Two lines that will never intersect7. Symbol for centimeter8. Number of inches in a foot9. 3 tens and 12 ones in standard form10. Value of 2 quarters, 3 dimes, and 1 nickel

1. $1.86 5. 85 miles;

2. 655 6. 312

3. 81 r 2 7. 1235

4. 114 miles 8. 31

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